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CONSTRUCTIONS BY RULER AND COMPASS, TOGETHER WITH A FIXED CONIC

Part of: Field extensions Real and complex geometry

Published online by Cambridge University Press:  08 March 2013

SEUNGJIN BAEK ,
INSONG CHOE ,
YOONHO JUNG ,
DONGWOOK LEE  and
JUNGGYO SEO
SEUNGJIN BAEK
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
INSONG CHOE*
Affiliation:
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-Gu, Seoul 143-701, Korea
YOONHO JUNG
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
DONGWOOK LEE
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
JUNGGYO SEO
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
*
✉ischoe@konkuk.ac.kr
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Abstract

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It is well known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from ancient times that these constructions can be performed when the use of several conic curves is allowed. In this paper, we prove that any point constructible from conics can be constructed using a ruler and a compass, together with a single fixed nondegenerate conic different from a circle.

Keywords

conic-constructible pointsruler and compassconicsgeometric construction

MSC classification

Secondary: 51M15: Geometric constructions 12F05: Algebraic extensions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 473 - 478
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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